Question 18

The district must hire 53 additional teachers.

To determine how many teachers the district needs to hire, we first calculate the total number of classes required by dividing the total student population by the maximum class size. With a student population of 6,734 and a maximum class size of 25, the district requires 269.36 classes, which rounds up to 270 classes. Since there are already 217 teachers, the district must hire 53 more teachers to meet this requirement.

A) 50

Choosing 50 teachers would only bring the total to 267 teachers, which would not be sufficient for the 270 classes needed. This option underestimates the number of teachers required to accommodate the student population, leading to larger class sizes than permitted.

B) 51

Hiring 51 teachers would result in a total of 268 teachers, still falling short of the 270 required. This option does not meet the needs of the student population and would also result in overcrowded classes, violating the maximum class size limit.

C) 53

Hiring 53 additional teachers would bring the total to 270 teachers, which is exactly what is needed to create classes of 25 students each for the total student population of 6,734. This option correctly fulfills the requirement based on the maximum class size, ensuring compliance with the district's policies.

D) 54

While hiring 54 teachers would result in 271 teachers, which technically exceeds the requirement, it is not the most efficient solution. This option does not accurately reflect the necessary number of teachers based on the student population and maximum class size, leading to unnecessary employment costs.

Conclusion

The correct answer is 53 teachers, as it precisely meets the requirement based on the calculations derived from the student population and class size limits. All other options either underestimate the number of teachers needed or exceed the necessary number without justification, demonstrating a clear understanding of the district's staffing needs.